Gian Antonio Susto

Alessio Arcudi, Davide Frizzo, Chiara Masiero et al.

Anomaly Detection (AD) focuses on identifying unusual behaviors in complex datasets. Machine Learning (ML) algorithms and Decision Support Systems (DSSs) provide effective solutions for AD, but detecting anomalies alone may not be enough, especially in engineering, where diagnostics and maintenance are crucial. Users need clear explanations to support root cause analysis and build trust in the model. The unsupervised nature of AD, however, makes interpretability a challenge. This paper introduces Extended Isolation Forest Feature Importance (ExIFFI), a method that explains predictions made by Extended Isolation Forest (EIF) models, which split data using hyperplanes. ExIFFI provides explanations at both global and local levels by leveraging feature importance. We also present an improved version, Enhanced Extended Isolation Forest (EIF+), designed to enhance the model's ability to detect unseen anomalies through a revised splitting strategy. Using five synthetic and eleven real-world datasets, we conduct a comparative analysis, evaluating unsupervised AD methods with the Average Precision metric. EIF+ consistently outperforms EIF across all datasets when trained without anomalies, demonstrating better generalization. To assess ExIFFI's interpretability, we introduce the Area Under the Curve of Feature Selection (AUC\_FS), a novel metric using feature selection as a proxy task. ExIFFI outperforms other unsupervised interpretability methods on 8 of 11 real-world datasets and successfully identifies anomalous features in synthetic datasets. When trained only on inliers, ExIFFI also outperforms competing models on real-world data and accurately detects anomalous features in synthetic datasets. We provide open-source code to encourage further research and reproducibility.

Lucas Costa Brito, Gian Antonio Susto, Jorge Nei Brito et al.

Artificial Intelligence (AI) is one of the approaches that has been proposed to analyze the collected data (e.g., vibration signals) providing a diagnosis of the asset's operating condition. It is known that models trained with labeled data (supervised) achieve excellent results, but two main problems make their application in production processes difficult: (i) impossibility or long time to obtain a sample of all operational conditions (since faults seldom happen) and (ii) high cost of experts to label all acquired data. Another limitating factor for the applicability of AI approaches in this context is the lack of interpretability of the models (black-boxes), which reduces the confidence of the diagnosis and trust/adoption from users. To overcome these problems, a new generic and interpretable approach for classifying faults in rotating machinery based on transfer learning from augmented synthetic data to real rotating machinery is here proposed, namelly FaultD-XAI (Fault Diagnosis using eXplainable AI). To provide scalability using transfer learning, synthetic vibration signals are created mimicking the characteristic behavior of failures in operation. The application of Gradient-weighted Class Activation Mapping (Grad-CAM) with 1D Convolutional Neural Network (1D CNN) allows the interpretation of results, supporting the user in decision making and increasing diagnostic confidence. The proposed approach not only obtained promising diagnostic performance, but was also able to learn characteristics used by experts to identify conditions in a source domain and apply them in another target domain. The experimental results suggest a promising approach on exploiting transfer learning, synthetic data and explainable artificial intelligence for fault diagnosis. Lastly, to guarantee reproducibility and foster research in the field, the developed dataset is made publicly available.

Francesco Pasti, Marina Ceccon, Davide Dalle Pezze et al.

While numerous methods achieving remarkable performance exist in the Object Detection literature, addressing data distribution shifts remains challenging. Continual Learning (CL) offers solutions to this issue, enabling models to adapt to new data while maintaining performance on previous data. This is particularly pertinent for edge devices, common in dynamic environments like automotive and robotics. In this work, we address the memory and computation constraints of edge devices in the Continual Learning for Object Detection (CLOD) scenario. Specifically, (i) we investigate the suitability of an open-source, lightweight, and fast detector, namely NanoDet, for CLOD on edge devices, improving upon larger architectures used in the literature. Moreover, (ii) we propose a novel CL method, called Latent Distillation~(LD), that reduces the number of operations and the memory required by state-of-the-art CL approaches without significantly compromising detection performance. Our approach is validated using the well-known VOC and COCO benchmarks, reducing the distillation parameter overhead by 74\% and the Floating Points Operations~(FLOPs) by 56\% per model update compared to other distillation methods.

Davide Dalle Pezze, Denis Deronjic, Chiara Masiero et al.

Continual Learning aims to learn from a stream of tasks, being able to remember at the same time both new and old tasks. While many approaches were proposed for single-class classification, multi-label classification in the continual scenario remains a challenging problem. For the first time, we study multi-label classification in the Domain Incremental Learning scenario. Moreover, we propose an efficient approach that has a logarithmic complexity with regard to the number of tasks, and can be applied also in the Class Incremental Learning scenario. We validate our approach on a real-world multi-label Alarm Forecasting problem from the packaging industry. For the sake of reproducibility, the dataset and the code used for the experiments are publicly available.

David Petrovic, Gian Antonio Susto, Angelo Cenedese

The commissioning of industrial electric drives still relies heavily on manual tuning of cascaded control loops, requiring expert knowledge and significant time. In this paper, we propose a fully automated approach for tuning the current control loop of industrial drives using Bayesian Optimization (BO) directly on real hardware, without requiring a system model or firmware modifications. The drive is treated as a black-box system, and the controller parameters are iteratively updated through closed-loop experiments. The tuning problem is formulated as a multi-objective optimization task that directly minimizes tracking error, time-weighted error, overshoot, and oscillatory behavior, enabling the identification of Pareto-optimal controller configurations. To address discrete parameters, noisy evaluations, and limited budgets, we adopt a multivariate Tree-structured Parzen Estimator (TPE) as the underlying BO strategy. The proposed method operates under practical industrial constraints, including communication latency and limited evaluation budgets. The experimental validation on a real motor drive system under no-load conditions shows that the method achieves performance comparable to expert tuning within a few minutes and without human intervention. Results show that Gaussian Process (GP)-based BO can yield highly competitive final solutions, but TPE-based BO is better aligned with this setting due to faster convergence, richer Pareto-front approximation, and lower computational overhead.

Davide Dalle Pezze, Eugenia Anello, Chiara Masiero et al.

Anomaly Detection is a relevant problem that arises in numerous real-world applications, especially when dealing with images. However, there has been little research for this task in the Continual Learning setting. In this work, we introduce a novel approach called SCALE (SCALing is Enough) to perform Compressed Replay in a framework for Anomaly Detection in Continual Learning setting. The proposed technique scales and compresses the original images using a Super Resolution model which, to the best of our knowledge, is studied for the first time in the Continual Learning setting. SCALE can achieve a high level of compression while maintaining a high level of image reconstruction quality. In conjunction with other Anomaly Detection approaches, it can achieve optimal results. To validate the proposed approach, we use a real-world dataset of images with pixel-based anomalies, with the scope to provide a reliable benchmark for Anomaly Detection in the context of Continual Learning, serving as a foundation for further advancements in the field.

Riccardo De Monte, Matteo Cederle, Gian Antonio Susto

State-of-the-art deep reinforcement learning (RL) methods have achieved remarkable performance in continuous control tasks, yet their computational complexity is often incompatible with the constraints of resource-limited hardware, due to their reliance on replay buffers, batch updates, and target networks. The emerging paradigm of streaming deep RL addresses this limitation through purely online updates, achieving strong empirical performance on standard benchmarks. In this work, we propose two novel streaming deep RL algorithms, Streaming Soft Actor-Critic (S2AC) and Streaming Deterministic Actor-Critic (SDAC), explicitly designed to be compatible with state-of-the-art batch RL methods, making them particularly suitable for on-device finetuning applications such as Sim2Real transfer. Both algorithms achieve performance comparable to state-of-the-art streaming baselines on standard benchmarks without requiring tedious per-environment hyperparameter tuning. We further investigate the batch-to-streaming transition, showing that a naive transition does not guarantee preservation of pre-trained policy performance, and propose a principled approach to address this challenge.

Riccardo De Monte, Davide Dalle Pezze, Marina Ceccon et al.

Continual Learning (CL) aims to learn new data while remembering previously acquired knowledge. In contrast to CL for image classification, CL for Object Detection faces additional challenges such as the missing annotations problem. In this scenario, images from previous tasks may contain instances of unknown classes that could reappear as labeled in future tasks, leading to task interference in replay-based approaches. Consequently, most approaches in the literature have focused on distillation-based techniques, which are effective when there is a significant class overlap between tasks. In our work, we propose an alternative to distillation-based approaches with a novel approach called Replay Consolidation with Label Propagation for Object Detection (RCLPOD). RCLPOD enhances the replay memory by improving the quality of the stored samples through a technique that promotes class balance while also improving the quality of the ground truth associated with these samples through a technique called label propagation. RCLPOD outperforms existing techniques on well-established benchmarks such as VOC and COC. Moreover, our approach is developed to work with modern architectures like YOLOv8, making it suitable for dynamic, real-world applications such as autonomous driving and robotics, where continuous learning and resource efficiency are essential.

Alessio Arcudi, Alessandro Ferreri, Francesco Borsatti et al.

Anomaly Detection (AD) is evolving through algorithms capable of identifying outliers in complex datasets. The Isolation Forest (IF), a pivotal AD technique, exhibits adaptability limitations and biases. This paper introduces the Function-based Isolation Forest (FuBIF), a generalization of IF that enables the use of real-valued functions for dataset branching, significantly enhancing the flexibility of evaluation tree construction. Complementing this, the FuBIF Feature Importance (FuBIFFI) algorithm extends the interpretability in IF-based approaches by providing feature importance scores across possible FuBIF models. This paper details the operational framework of FuBIF, evaluates its performance against established methods, and explores its theoretical contributions. An open-source implementation is provided to encourage further research and ensure reproducibility.

Francesco Pasti, Riccardo De Monte, Davide Dalle Pezze et al.

Detecting objects in mobile robotics is crucial for numerous applications, from autonomous navigation to inspection. However, robots often need to operate in different domains from those they were trained in, requiring them to adjust to these changes. Tiny mobile robots, subject to size, power, and computational constraints, encounter even more difficulties in running and adapting these algorithms. Such adaptability, though, is crucial for real-world deployment, where robots must operate effectively in dynamic and unpredictable settings. In this work, we introduce a novel benchmark to evaluate the continual learning capabilities of object detection systems in tiny robotic platforms. Our contributions include: (i) Tiny Robotics Object Detection~(TiROD), a comprehensive dataset collected using the onboard camera of a small mobile robot, designed to test object detectors across various domains and classes; (ii) a benchmark of different continual learning strategies on this dataset using NanoDet, a lightweight object detector. Our results highlight key challenges in developing robust and efficient continual learning strategies for object detectors in tiny robotics.

Natalie Gentner, Gian Antonio Susto

Process monitoring and control are essential in modern industries for ensuring high quality standards and optimizing production performance. These technologies have a long history of application in production and have had numerous positive impacts, but also hold great potential when integrated with Industry 4.0 and advanced machine learning, particularly deep learning, solutions. However, in order to implement these solutions in production and enable widespread adoption, the scalability and transferability of deep learning methods have become a focus of research. While transfer learning has proven successful in many cases, particularly with computer vision and homogenous data inputs, it can be challenging to apply to heterogeneous data. Motivated by the need to transfer and standardize established processes to different, non-identical environments and by the challenge of adapting to heterogeneous data representations, this work introduces the Domain Adaptation Neural Network with Cyclic Supervision (DBACS) approach. DBACS addresses the issue of model generalization through domain adaptation, specifically for heterogeneous data, and enables the transfer and scalability of deep learning-based statistical control methods in a general manner. Additionally, the cyclic interactions between the different parts of the model enable DBACS to not only adapt to the domains, but also match them. To the best of our knowledge, DBACS is the first deep learning approach to combine adaptation and matching for heterogeneous data settings. For comparison, this work also includes subspace alignment and a multi-view learning that deals with heterogeneous representations by mapping data into correlated latent feature spaces. Finally, DBACS with its ability to adapt and match, is applied to a virtual metrology use case for an etching process run on different machine types in semiconductor manufacturing.

Elisa Marcelli, Tommaso Barbariol, Gian Antonio Susto

The detection of anomalous behaviours is an emerging need in many applications, particularly in contexts where security and reliability are critical aspects. While the definition of anomaly strictly depends on the domain framework, it is often impractical or too time consuming to obtain a fully labelled dataset. The use of unsupervised models to overcome the lack of labels often fails to catch domain specific anomalies as they rely on general definitions of outlier. This paper suggests a new active learning based approach, ALIF, to solve this problem by reducing the number of required labels and tuning the detector towards the definition of anomaly provided by the user. The proposed approach is particularly appealing in the presence of a Decision Support System (DSS), a case that is increasingly popular in real-world scenarios. While it is common that DSS embedded with anomaly detection capabilities rely on unsupervised models, they don't have a way to improve their performance: ALIF is able to enhance the capabilities of DSS by exploiting the user feedback during common operations. ALIF is a lightweight modification of the popular Isolation Forest that proved superior performances with respect to other state-of-art algorithms in a multitude of real anomaly detection datasets.

Tommaso Barbariol, Davide Masiero, Enrico Feltresi et al.

An Anomaly Detection (AD) System for Self-diagnosis has been developed for Multiphase Flow Meter (MPFM). The system relies on machine learning algorithms for time series forecasting, historical data have been used to train a model and to predict the behavior of a sensor and, thus, to detect anomalies.

Mattia Carletti, Matteo Terzi, Gian Antonio Susto

Adversarial Training has proved to be an effective training paradigm to enforce robustness against adversarial examples in modern neural network architectures. Despite many efforts, explanations of the foundational principles underpinning the effectiveness of Adversarial Training are limited and far from being widely accepted by the Deep Learning community. In this paper, we describe surprising properties of adversarially-trained models, shedding light on mechanisms through which robustness against adversarial attacks is implemented. Moreover, we highlight limitations and failure modes affecting these models that were not discussed by prior works. We conduct extensive analyses on a wide range of architectures and datasets, performing a deep comparison between robust and natural models.

Fabrizio Genilotti, Arianna Stropeni, Gionata Grotto et al.

The reliability of a machine vision system for autonomous driving depends heavily on its training data distribution. When a vehicle encounters significantly different conditions, such as atypical obstacles, its perceptual capabilities can degrade substantially. Unlike many domains where errors carry limited consequences, failures in autonomous driving translate directly into physical risk for passengers, pedestrians, and other road users. To address this challenge, we explore Visual Anomaly Detection (VAD) as a solution. VAD enables the identification of anomalous objects not present during training, allowing the system to alert the driver when an unfamiliar situation is detected. Crucially, VAD models produce pixel-level anomaly maps that can guide driver attention to specific regions of concern without requiring any prior assumptions about the nature or form of the hazard. We benchmark eight state-of-the-art VAD methods on AnoVox, the largest synthetic dataset for anomaly detection in autonomous driving. In particular, we evaluate performance across four backbone architectures spanning from large networks to lightweight ones such as MobileNet and DeiT-Tiny. Our results demonstrate that VAD transfers effectively to road scenes. Notably, Tiny-Dinomaly achieves the best accuracy-efficiency trade-off for edge deployment, matching full-scale localization performance at a fraction of the memory cost. This study represents a concrete step toward safer, more responsible deployment of autonomous vehicles, ultimately improving protection for passengers, pedestrians, and all road users.

Emad Efatinasab, Nahal Azadi, Davide Dalle Pezze et al.

As smart grids evolve to meet growing energy demands and modern operational challenges, the ability to accurately predict faults becomes increasingly critical. However, existing AI-based fault prediction models struggle to ensure reliability in evolving environments where they are required to adapt to new fault types and operational zones. In this paper, we propose a continual learning (CL) framework in the smart grid context to evolve the model together with the environment. We design four realistic evaluation scenarios grounded in class-incremental and domain-incremental learning to emulate evolving grid conditions. We further introduce Prototype-based Dark Experience Replay (ProDER), a unified replay-based approach that integrates prototype-based feature regularization, logit distillation, and a prototype-guided replay memory. ProDER achieves the best performance among tested CL techniques, with only a 0.045 accuracy drop for fault type prediction and 0.015 for fault zone prediction. These results demonstrate the practicality of CL for scalable, real-world fault prediction in smart grids.

Marco Calì, Alberto Sinigaglia, Niccolò Turcato et al.

In the following report, we describe the solution we propose for the AI Olympics competition held at IROS 2024. Our solution is based on a Model-free Deep Reinforcement Learning approach combined with an evolutionary strategy. We will briefly describe the algorithms that have been used and then provide details of the approach

Manuel Barusco, Francesco Borsatti, David Petrovic et al.

Visual Anomaly Detection (VAD) is a critical task for many applications including industrial inspection and healthcare. While VAD has been extensively studied, two key challenges remain largely unaddressed in conjunction: edge deployment, where computational resources are severely constrained, and continual learning, where models must adapt to evolving data distributions without forgetting previously acquired knowledge. Our benchmark provides guidance for the selection of the optimal backbone and VAD method under joint efficiency and adaptability constraints, characterizing the trade-offs between memory footprint, inference cost, and detection performance. Studying these challenges in isolation is insufficient, as methods designed for one setting make assumptions that break down when the other constraint is simultaneously imposed. In this work, we propose the first comprehensive benchmark for VAD on the edge in the continual learning scenario, evaluating seven VAD models across three lightweight backbone architectures. Furthermore, we propose Tiny-Dinomaly, a lightweight adaptation of the Dinomaly model built on the DINO foundation model that achieves 13x smaller memory footprint and 20x lower computational cost while improving Pixel F1 by 5 percentage points. Finally, we introduce targeted modifications to PatchCore and PaDiM to improve their efficiency in the continual learning setting.

Arianna Stropeni, Fabrizio Genilotti, Francesco Borsatti et al.

Visual Anomaly Detection (VAD) is essential for industrial quality control, enabling automatic defect detection in manufacturing. In real production lines, VAD systems must satisfy strict real-time and privacy requirements, necessitating a shift from cloud-based processing to local edge deployment. However, processing data locally on edge devices introduces new challenges because edge hardware has limited memory and computational resources. To overcome these limitations, we propose two efficient VAD methods designed for edge deployment: PatchCore-Lite and Padim-Lite, based on the popular PatchCore and PaDiM models. PatchCore-Lite runs first a coarse search on a product-quantized memory bank, then an exact search on a decoded subset. Padim-Lite is sped up using diagonal covariance, turning Mahalanobis distance into efficient element-wise computation. We evaluate our methods on the MVTec AD and VisA benchmarks and show their suitability for edge environments. PatchCore-Lite achieves a remarkable 79% reduction in total memory footprint, while PaDiM-Lite achieves substantial efficiency gains with a 77% reduction in total memory and a 31% decrease in inference time. These results show that VAD can be effectively deployed on edge devices, enabling real-time, private, and cost-efficient industrial inspection.

Matteo Cederle, Saverio Bolognani, Gian Antonio Susto

Mobility-on-demand systems like ride-hailing have transformed urban transportation, but they have also exacerbated socio-economic inequalities in access to these services, also due to surge pricing strategies. Although several fairness-aware frameworks have been proposed in smart mobility, they often overlook the temporal and situational variability of user urgency that shapes real-world transportation demands. This paper introduces a non-monetary, Karma-based mechanism that models endogenous urgency, allowing user time-sensitivity to evolve in response to system conditions as well as external factors. We develop a theoretical framework maintaining the efficiency and fairness guarantees of classical Karma economies, while accommodating this realistic user behavior modeling. Applied to a simplified simulated mobility-on-demand scenario, we provide a proof-of-concept illustration of the proposed framework, showing that it exhibits promising behavior in terms of system efficiency and equitable resource allocation, while acknowledging that a full treatment of realistic MoD complexity remains an important direction for future work.

Davide Frizzo, Fabrizio Genilotti, David Petrovic et al.

Virtual Reality (VR) applications require robust user identification systems to ensure secure access to equipment and protect worker identities. Motion tracking data from VR headsets and controllers has emerged as a powerful behavioral biometric, with recent studies demonstrating identification accuracies exceeding 94% across a large user base. However, the application of modern deep learning architectures, particularly State Space Models (SSM), to VR scenarios remains largely unexplored. In this work, we benchmark user identification performance across the large-scale Who is Alyx VR dataset, gathering data from 71 users playing the popular Half-Life:Alyx game. We evaluate both established architectures (Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Convolutional Neural Network (CNN), Temporal Convolutional Network (TCN), Transformer) and the emerging SSMs on time series motion data. Our results provide the first comprehensive benchmark of state-of-the-art and novel architectures for VR user identification, establishing baseline performance metrics for future privacy preserving authentication systems in manufacturing environments.

Manuel Barusco, Davide Dalle Pezze, Francesco Borsatti et al.

Visual Anomaly Detection (VAD) is crucial for industrial inspection, yet most existing methods are limited to single-category scenarios, failing to address the multi-class and continual learning demands of real-world environments. While Teacher-Student (TS) architectures are efficient, they remain unexplored for the Continual Setting. To bridge this gap, we propose AdapTS, a unified TS framework designed for multi-class and continual settings, optimized for edge deployment. AdapTS eliminates the need for two different architectures by utilizing a single shared frozen backbone and injecting lightweight trainable adapters into the student pathway. Training is enhanced via a segmentation-guided objective and synthetic Perlin noise, while a prototype-based task identification mechanism dynamically selects adapters at inference with 99\% accuracy. Experiments on MVTec AD and VisA demonstrate that AdapTS matches the performance of existing TS methods across multi-class and continual learning scenarios, while drastically reducing memory overhead. Our lightest variant, AdapTS-S, requires only 8 MB of additional memory, 13x less than STFPM (95 MB), 48x less than RD4AD (360 MB), and 149x less than DeSTSeg (1120 MB), making it a highly scalable solution for edge deployment in complex industrial environments.

Edoardo Scarpel, Alberto Pettena, Matteo Cederle et al.

This paper proposes a fully dynamic Deep Reinforcement Learning (DRL) method for rebalancing dockless bike-sharing systems, overcoming the limitations of periodic, system-wide interventions. We model the service through a graph-based simulator and cast rebalancing as a Markov decision process. A DRL agent routes a single truck in real time, executing localized pick-up, drop-off, and charging actions guided by spatiotemporal criticality scores. Experiments on real-world data show significant reductions in availability failures with a minimal fleet size, while limiting spatial inequality and mobility deserts. Our approach demonstrates the value of learning-based rebalancing for efficient and reliable shared micromobility.

Fabrizio Genilotti, Arianna Stropeni, Francesco Borsatti et al.

Space missions generate massive volumes of high-resolution orbital and surface imagery that far exceed the capacity for manual inspection. Detecting rare phenomena is scientifically critical, yet traditional supervised learning struggles due to scarce labeled examples and closed-world assumptions that prevent discovery of genuinely novel observations. In this work, we investigate Visual Anomaly Detection (VAD) as a framework for automated discovery in planetary exploration. We present the first empirical evaluation of state-of-the-art feature-based VAD methods on real planetary imagery, encompassing both orbital lunar data and Mars rover surface imagery. To support this evaluation, we introduce two benchmarks: (i) a lunar dataset derived from Lunar Reconnaissance Orbiter Camera Narrow Angle imagery, comprising of fresh and degraded craters as anomalies alongside normal terrain; and (ii) a Mars surface dataset designed to reflect the characteristics of rover-acquired imagery. We evaluate multiple VAD approaches with a focus on computationally efficient, edge-oriented solutions suitable for onboard deployment, applicable to both orbital platforms surveying the lunar surface and surface rovers operating on Mars. Our results demonstrate that feature-based VAD methods can effectively identify rare planetary surface phenomena while remaining feasible for resource-constrained environments. By grounding anomaly detection in planetary science, this work establishes practical benchmarks and highlights the potential of open-world perception systems to support a range of mission-critical applications, including tactical planning, landing site selection, hazard detection, bandwidth-aware data prioritization, and the discovery of unanticipated geological processes.

Jinwei Hu, Francesco Borsatti, Arianna Stropeni et al.

Industrial visual anomaly detection (VAD) methods are typically trained on normal samples only, yet performance improves substantially when even limited anomalous data is available. Existing anomaly generation approaches either require real anomalous examples, demand expensive hardware, or produce synthetic defects that lack realism. We present MIRAGE (Model-agnostic Industrial Realistic Anomaly Generation and Evaluation), a fully automated pipeline for realistic anomalous image generation and pixel-level mask creation that requires no training and no anomalous images. Our pipeline accesses any generative model as a black box via API calls, uses a VLM for automatic defect prompt generation, and includes a CLIP-based quality filter to retain only well-aligned generated images. For mask generation at scale, we introduce a lightweight, training-free dual-branch semantic change detection module combining text-conditioned Grounding DINO features with fine-grained YOLOv26-Seg structural features. We benchmark four generation methods using Gemini 2.5 Flash Image (Nano Banana) as the generative backbone, evaluating performance on MVTec AD and VisA across two distinct tasks: (i) downstream anomaly segmentation and (ii) visual quality of the generated images, assessed via standard metrics (IS, IC-LPIPS) and a human perceptual study involving 31 participants and 1,550 pairwise votes. The results demonstrate that MIRAGE offers a scalable, accessible foundation for anomaly-aware industrial inspection that requires no real defect data. As a final contribution, we publicly release a large-scale dataset comprising 500 image-mask pairs per category for every MVTec AD and VisA class, over 13,000 pairs in total, alongside all generation prompts and pipeline code.

Matteo Cederle, Luca Vittorio Piron, Marina Ceccon et al.

As Machine Learning grows in popularity across various fields, equity has become a key focus for the AI community. However, fairness-oriented approaches are still underexplored in smart mobility. Addressing this gap, our study investigates the balance between performance optimization and algorithmic fairness in shared micromobility services providing a novel framework based on Reinforcement Learning. Exploiting Q-learning, the proposed methodology achieves equitable outcomes in terms of the Gini index across different areas characterized by their distance from central hubs. Through vehicle rebalancing, the provided scheme maximizes operator performance while ensuring fairness principles for users, reducing iniquity by up to 85% while only increasing costs by 30% (w.r.t. applying no equity adjustment). A case study with synthetic data validates our insights and highlights the importance of fairness in urban micromobility (source code: https://github.com/mcederle99/FairMSS.git).

Luca Della Libera, Jacopo Andreoli, Davide Dalle Pezze et al.

A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive performance. However, in order to optimally plan maintenance operations, it is also important to quantify the uncertainty inherent to the predictions. This issue can be addressed by turning standard frequentist neural networks into Bayesian neural networks, which are naturally capable of providing confidence intervals around the estimates. Several methods exist for training those models. Researchers have focused mostly on parametric variational inference and sampling-based techniques, which notoriously suffer from limited approximation power and large computational burden, respectively. In this work, we use Stein variational gradient descent, a recently proposed algorithm for approximating intractable distributions that overcomes the drawbacks of the aforementioned techniques. In particular, we show through experimental studies on simulated run-to-failure turbofan engine degradation data that Bayesian deep learning models trained via Stein variational gradient descent consistently outperform with respect to convergence speed and predictive performance both the same models trained via parametric variational inference and their frequentist counterparts trained via backpropagation. Furthermore, we propose a method to enhance performance based on the uncertainty information provided by the Bayesian models. We release the source code at https://github.com/lucadellalib/bdl-rul-svgd.

Matteo Cederle, Giacomo Scatto, Gian Antonio Susto

Urban traffic congestion presents a significant challenge for modern cities, which impacts mobility and sustainability. Traditional traffic light control systems often fail to adapt to dynamic conditions, leading to inefficiencies. This paper proposes a novel deep reinforcement learning agent for traffic light control that addresses this limitation by explicitly integrating fairness considerations for both vehicular and pedestrian traffic. Unlike prior work, our approach dynamically balances these flows based on real-time demand, moving beyond systems focused solely on vehicles. Experimental results demonstrate that our agent effectively reduces congestion while ensuring equitable service for both the categories of road users. This research contributes to a practical and adaptable solution for intelligent traffic management within the framework of smart cities, paving the way for more efficient and inclusive urban mobility.

Matteo Cederle, Saverio Bolognani, Gian Antonio Susto

Dynamic Population Games (DPGs) provide a tractable framework for modeling strategic interactions in large populations of self-interested agents, and have been successfully applied to the design of Karma economies, a class of fair non-monetary resource allocation mechanisms. Despite their appealing theoretical properties, existing computational tools for DPGs assume full knowledge of the game model and operate in a centralized fashion, limiting their applicability in realistic settings where agents have access only to their own private experience. This paper takes a step towards addressing this gap by studying model-free equilibrium learning in Karma DPGs. First, we analyze the setting in which a novel agent joins a Karma DPG already at its Stationary Nash Equilibrium (SNE) and learns a policy via Deep Q-Networks (DQN) without knowledge of the game model. Leveraging recent convergence results for DQN, we establish a suboptimality bound consisting of a DQN approximation error of order $O(1/\sqrt{N_s})$ and a mean field perturbation error of order $O(1/N)$, where $N_s$ is the replay buffer size and $N$ is the population size. Second, we consider the challenging problem of learning the SNE from scratch. We show empirically that combining deep RL with fictitious play and smoothed policy iteration allows agents to converge, in a model-free fashion, to a configuration close to the centrally computed SNE. Together, these contributions support the vision of Karma economies as practical tools for fair resource allocation.

Firas Mohamed Elamine Kiram, Imane Youkana, Rachida Saouli et al.

Chemotherapy dose optimization can be formulated as a dynamic treatment regime, requiring sequential decisions under uncertainty that must balance tumor suppression against toxicity. However, most reinforcement learning approaches assume full observability of the patient state, a condition rarely met in clinical practice. We investigate whether memory-augmented policies can improve chemotherapy control under partial observability. To this end, we employ a recurrent TD3-based approach with separate LSTM actor-critic networks and evaluate it on the AhnChemoEnv benchmark from DTR-Bench, considering both off-policy and on-policy recurrent architectures against feed-forward TD3 and Soft Actor-Critic. Pharmacokinetic and pharmacodynamic variability are held fixed to isolate hidden-state uncertainty and observation noise and to avoid confounding effects from inter-patient variability. Across ten random seeds, recurrence yields modest benefit under full observability but substantially stronger and more stable performance under partial observability, with more consistent tumor suppression and improved normal-cell preservation. These findings indicate that memory-based policies are particularly beneficial when clinically relevant state information is incomplete or noisy.

Marina Ceccon, Davide Dalle Pezze, Alessandro Fabris et al.

Despite the critical importance of the medical domain in Deep Learning, most of the research in this area solely focuses on training models in static environments. It is only in recent years that research has begun to address dynamic environments and tackle the Catastrophic Forgetting problem through Continual Learning (CL) techniques. Previous studies have primarily focused on scenarios such as Domain Incremental Learning and Class Incremental Learning, which do not fully capture the complexity of real-world applications. Therefore, in this work, we propose a novel benchmark combining the challenges of new class arrivals and domain shifts in a single framework, by considering the New Instances and New Classes (NIC) scenario. This benchmark aims to model a realistic CL setting for the multi-label classification problem in medical imaging. Additionally, it encompasses a greater number of tasks compared to previously tested scenarios. Specifically, our benchmark consists of two datasets (NIH and CXP), nineteen classes, and seven tasks, a stream longer than the previously tested ones. To solve common challenges (e.g., the task inference problem) found in the CIL and NIC scenarios, we propose a novel approach called Replay Consolidation with Label Propagation (RCLP). Our method surpasses existing approaches, exhibiting superior performance with minimal forgetting.

Manuel Barusco, Francesco Borsatti, Davide Dalle Pezze et al.

Visual Anomaly Detection (VAD) has gained significant research attention for its ability to identify anomalous images and pinpoint the specific areas responsible for the anomaly. A key advantage of VAD is its unsupervised nature, which eliminates the need for costly and time-consuming labeled data collection. However, despite its potential for real-world applications, the literature has given limited focus to resource-efficient VAD, particularly for deployment on edge devices. This work addresses this gap by leveraging lightweight neural networks to reduce memory and computation requirements, enabling VAD deployment on resource-constrained edge devices. We benchmark the major VAD algorithms within this framework and demonstrate the feasibility of edge-based VAD using the well-known MVTec dataset. Furthermore, we introduce a novel algorithm, Partially Shared Teacher-student (PaSTe), designed to address the high resource demands of the existing Student Teacher Feature Pyramid Matching (STFPM) approach. Our results show that PaSTe decreases the inference time by 25%, while reducing the training time by 33% and peak RAM usage during training by 76%. These improvements make the VAD process significantly more efficient, laying a solid foundation for real-world deployment on edge devices.

Riccardo De Monte, Davide Dalle Pezze, Gian Antonio Susto

Real-time object detectors like YOLO achieve exceptional performance when trained on large datasets for multiple epochs. However, in real-world scenarios where data arrives incrementally, neural networks suffer from catastrophic forgetting, leading to a loss of previously learned knowledge. To address this, prior research has explored strategies for Class Incremental Learning (CIL) in Continual Learning for Object Detection (CLOD), with most approaches focusing on two-stage object detectors. However, existing work suggests that Learning without Forgetting (LwF) may be ineffective for one-stage anchor-free detectors like YOLO due to noisy regression outputs, which risk transferring corrupted knowledge. In this work, we introduce YOLO LwF, a self-distillation approach tailored for YOLO-based continual object detection. We demonstrate that when coupled with a replay memory, YOLO LwF significantly mitigates forgetting. Compared to previous approaches, it achieves state-of-the-art performance, improving mAP by +2.1% and +2.9% on the VOC and COCO benchmarks, respectively.

Manuel Barusco, Lorenzo D'Antoni, Davide Dalle Pezze et al.

Visual Anomaly Detection (VAD) is a critical task in computer vision with numerous real-world applications. However, deploying these models on edge devices presents significant challenges, such as constrained computational and memory resources. Additionally, dynamic data distributions in real-world settings necessitate continuous model adaptation, further complicating deployment under limited resources. To address these challenges, we present a novel investigation into the problem of Continual Learning for Visual Anomaly Detection (CLAD) on edge devices. We evaluate the STFPM approach, given its low memory footprint on edge devices, which demonstrates good performance when combined with the Replay approach. Furthermore, we propose to study the behavior of a recently proposed approach, PaSTe, specifically designed for the edge but not yet explored in the Continual Learning context. Our results show that PaSTe is not only a lighter version of STPFM, but it also achieves superior anomaly detection performance, improving the f1 pixel performance by 10% with the Replay technique. In particular, the structure of PaSTe allows us to test it using a series of Compressed Replay techniques, reducing memory overhead by a maximum of 91.5% compared to the traditional Replay for STFPM. Our study proves the feasibility of deploying VAD models that adapt and learn incrementally on CLAD scenarios on resource-constrained edge devices.

Matteo Cederle, Marco Fabris, Gian Antonio Susto

Autonomous intersection management (AIM) poses significant challenges due to the intricate nature of real-world traffic scenarios and the need for a highly expensive centralised server in charge of simultaneously controlling all the vehicles. This study addresses such issues by proposing a novel distributed approach to AIM utilizing multi-agent reinforcement learning (MARL). We show that by leveraging the 3D surround view technology for advanced assistance systems, autonomous vehicles can accurately navigate intersection scenarios without needing any centralised controller. The contributions of this paper thus include a MARL-based algorithm for the autonomous management of a 4-way intersection and also the introduction of a new strategy called prioritised scenario replay for improved training efficacy. We validate our approach as an innovative alternative to conventional centralised AIM techniques, ensuring the full reproducibility of our results. Specifically, experiments conducted in virtual environments using the SMARTS platform highlight its superiority over benchmarks across various metrics.

Valentina Zaccaria, David Dandolo, Chiara Masiero et al.

Pursuing fast and robust interpretability in Anomaly Detection is crucial, especially due to its significance in practical applications. Traditional Anomaly Detection methods excel in outlier identification but are often black-boxes, providing scant insights into their decision-making process. This lack of transparency compromises their reliability and hampers their adoption in scenarios where comprehending the reasons behind anomaly detection is vital. At the same time, getting explanations quickly is paramount in practical scenarios. To bridge this gap, we present AcME-AD, a novel approach rooted in Explainable Artificial Intelligence principles, designed to clarify Anomaly Detection models for tabular data. AcME-AD transcends the constraints of model-specific or resource-heavy explainability techniques by delivering a model-agnostic, efficient solution for interoperability. It offers local feature importance scores and a what-if analysis tool, shedding light on the factors contributing to each anomaly, thus aiding root cause analysis and decision-making. This paper elucidates AcME-AD's foundation, its benefits over existing methods, and validates its effectiveness with tests on both synthetic and real datasets. AcME-AD's implementation and experiment replication code is accessible in a public repository.

Valentina Zaccaria, Chiara Masiero, David Dandolo et al.

While Machine Learning has become crucial for Industry 4.0, its opaque nature hinders trust and impedes the transformation of valuable insights into actionable decision, a challenge exacerbated in the evolving Industry 5.0 with its human-centric focus. This paper addresses this need by testing the applicability of AcME-AD in industrial settings. This recently developed framework facilitates fast and user-friendly explanations for anomaly detection. AcME-AD is model-agnostic, offering flexibility, and prioritizes real-time efficiency. Thus, it seems suitable for seamless integration with industrial Decision Support Systems. We present the first industrial application of AcME-AD, showcasing its effectiveness through experiments. These tests demonstrate AcME-AD's potential as a valuable tool for explainable AD and feature-based root cause analysis within industrial environments, paving the way for trustworthy and actionable insights in the age of Industry 5.0.

Marina Ceccon, Giandomenico Cornacchia, Davide Dalle Pezze et al.

Undesirable biases encoded in the data are key drivers of algorithmic discrimination. Their importance is widely recognized in the algorithmic fairness literature, as well as legislation and standards on anti-discrimination in AI. Despite this recognition, data biases remain understudied, hindering the development of computational best practices for their detection and mitigation. In this work, we present three common data biases and study their individual and joint effect on algorithmic discrimination across a variety of datasets, models, and fairness measures. We find that underrepresentation of vulnerable populations in training sets is less conducive to discrimination than conventionally affirmed, while combinations of proxies and label bias can be far more critical. Consequently, we develop dedicated mechanisms to detect specific types of bias, and combine them into a preliminary construct we refer to as the Data Bias Profile (DBP). This initial formulation serves as a proof of concept for how different bias signals can be systematically documented. Through a case study with popular fairness datasets, we demonstrate the effectiveness of the DBP in predicting the risk of discriminatory outcomes and the utility of fairness-enhancing interventions. Overall, this article bridges algorithmic fairness research and anti-discrimination policy through a data-centric lens.

Arianna Stropeni, Francesco Borsatti, Manuel Barusco et al.

Visual Anomaly Detection (VAD) is a key task in industrial settings, where minimizing operational costs is essential. Deploying deep learning models within Internet of Things (IoT) environments introduces specific challenges due to limited computational power and bandwidth of edge devices. This study investigates how to perform VAD effectively under such constraints by leveraging compact, efficient processing strategies. We evaluate several data compression techniques, examining the tradeoff between system latency and detection accuracy. Experiments on the MVTec AD benchmark demonstrate that significant compression can be achieved with minimal loss in anomaly detection performance compared to uncompressed data. Current results show up to 80% reduction in end-to-end inference time, including edge processing, transmission, and server computation.

Niccolò Turcato, Alberto Sinigaglia, Alberto Dalla Libera et al.

Continuous control Deep Reinforcement Learning (RL) approaches are known to suffer from estimation biases, leading to suboptimal policies. This paper introduces innovative methods in RL, focusing on addressing and exploiting estimation biases in Actor-Critic methods for continuous control tasks, using Deep Double Q-Learning. We design a Bias Exploiting (BE) mechanism to dynamically select the most advantageous estimation bias during training of the RL agent. Most State-of-the-art Deep RL algorithms can be equipped with the BE mechanism, without hindering performance or computational complexity. Our extensive experiments across various continuous control tasks demonstrate the effectiveness of our approaches. We show that RL algorithms equipped with this method can match or surpass their counterparts, particularly in environments where estimation biases significantly impact learning. The results underline the importance of bias exploitation in improving policy learning in RL.

Manuel Barusco, Francesco Borsatti, Davide Dalle Pezze et al.

Recent advances in Visual Anomaly Detection (VAD) have introduced sophisticated algorithms leveraging embeddings generated by pre-trained feature extractors. Inspired by these developments, we investigate the adaptation of such algorithms to the audio domain to address the problem of Audio Anomaly Detection (AAD). Unlike most existing AAD methods, which primarily classify anomalous samples, our approach introduces fine-grained temporal-frequency localization of anomalies within the spectrogram, significantly improving explainability. This capability enables a more precise understanding of where and when anomalies occur, making the results more actionable for end users. We evaluate our approach on industrial and environmental benchmarks, demonstrating the effectiveness of VAD techniques in detecting anomalies in audio signals. Moreover, they improve explainability by enabling localized anomaly identification, making audio anomaly detection systems more interpretable and practical.

Mattia Fanan, Davide Dalle Pezze, Emad Efatinasab et al.

Behavior-based Driver Identification is an emerging technology that recognizes drivers based on their unique driving behaviors, offering important applications such as vehicle theft prevention and personalized driving experiences. However, most studies fail to account for the real-world challenges of deploying Deep Learning models within vehicles. These challenges include operating under limited computational resources, adapting to new drivers, and changes in driving behavior over time. The objective of this study is to evaluate if Continual Learning (CL) is well-suited to address these challenges, as it enables models to retain previously learned knowledge while continually adapting with minimal computational overhead and resource requirements. We tested several CL techniques across three scenarios of increasing complexity based on the well-known OCSLab dataset. This work provides an important step forward in scalable driver identification solutions, demonstrating that CL approaches, such as DER, can obtain strong performance, with only an 11% reduction in accuracy compared to the static scenario. Furthermore, to enhance the performance, we propose two new methods, SmooER and SmooDER, that leverage the temporal continuity of driver identity over time to enhance classification accuracy. Our novel method, SmooDER, achieves optimal results with only a 2% reduction compared to the 11\% of the DER approach. In conclusion, this study proves the feasibility of CL approaches to address the challenges of Driver Identification in dynamic environments, making them suitable for deployment on cloud infrastructure or directly within vehicles.

Marina Ceccon, Davide Dalle Pezze, Alessandro Fabris et al.

Deep Learning has advanced significantly in medical applications, aiding disease diagnosis in Chest X-ray images. However, expanding model capabilities with new data remains a challenge, which Continual Learning (CL) aims to address. Previous studies have evaluated CL strategies based on classification performance; however, in sensitive domains such as healthcare, it is crucial to assess performance across socially salient groups to detect potential biases. This study examines how bias evolves across tasks using domain-specific fairness metrics and how different CL strategies impact this evolution. Our results show that Learning without Forgetting and Pseudo-Label achieve optimal classification performance, but Pseudo-Label is less biased.

Arianna Stropeni, Valentina Zaccaria, Francesco Borsatti et al.

In recent years, Visual Anomaly Detection (VAD) has gained significant attention due to its ability to identify anomalous images using only normal images during training. Many VAD models work without supervision but are still able to provide visual explanations by highlighting the anomalous regions within an image. However, although these visual explanations can be helpful, they lack a direct and semantically meaningful interpretation for users. To address this limitation, we propose extending Concept Bottleneck Models (CBMs) to the VAD setting. By learning meaningful concepts, the network can provide human-interpretable descriptions of anomalies, offering a novel and more insightful way to explain them. Our contributions are threefold: (i) we develop a Concept Dataset to support research on CBMs for VAD; (ii) we improve the CBM architecture to generate both concept-based and visual explanations, bridging semantic and localization interpretability; and (iii) we introduce a pipeline for synthesizing artificial anomalies, preserving the VAD paradigm of minimizing dependence on rare anomalous samples. Our approach, Concept-Aware Visual Anomaly Detection (CONVAD), achieves performance comparable to classic VAD methods while providing richer, concept-driven explanations that enhance interpretability and trust in VAD systems.

Marina Ceccon, Alessandro Fabris, Goran Radanović et al.

Algorithmic recourse seeks to provide individuals with actionable recommendations that increase their chances of receiving favorable outcomes from automated decision systems (e.g., loan approvals). While prior research has emphasized robustness to model updates, considerably less attention has been given to the temporal dynamics of recourse--particularly in competitive, resource-constrained settings where recommendations shape future applicant pools. In this work, we present a novel time-aware framework for algorithmic recourse, explicitly modeling how candidate populations adapt in response to recommendations. Additionally, we introduce a novel reinforcement learning (RL)-based recourse algorithm that captures the evolving dynamics of the environment to generate recommendations that are both feasible and valid. We design our recommendations to be durable, supporting validity over a predefined time horizon T. This durability allows individuals to confidently reapply after taking time to implement the suggested changes. Through extensive experiments in complex simulation environments, we show that our approach substantially outperforms existing baselines, offering a superior balance between feasibility and long-term validity. Together, these results underscore the importance of incorporating temporal and behavioral dynamics into the design of practical recourse systems.

Manuel Barusco, Francesco Borsatti, Nicola Beda et al.

Visual Anomaly Detection (VAD) seeks to identify abnormal images and precisely localize the corresponding anomalous regions, relying solely on normal data during training. This approach has proven essential in domains such as manufacturing and, more recently, in the medical field, where accurate and explainable detection is critical. Despite its importance, the impact of evolving input data distributions over time has received limited attention, even though such changes can significantly degrade model performance. In particular, given the dynamic and evolving nature of medical imaging data, Continual Learning (CL) provides a natural and effective framework to incrementally adapt models while preserving previously acquired knowledge. This study explores for the first time the application of VAD models in a CL scenario for the medical field. In this work, we utilize a CL version of the well-established PatchCore model, called PatchCoreCL, and evaluate its performance using BMAD, a real-world medical imaging dataset with both image-level and pixel-level annotations. Our results demonstrate that PatchCoreCL is an effective solution, achieving performance comparable to the task-specific models, with a forgetting value less than a 1%, highlighting the feasibility and potential of CL for adaptive VAD in medical imaging.

Alessio Arcudi, Davide Sartor, Alberto Sinigaglia et al.

This paper introduces MANGO (Multilayer Abstraction for Nested Generation of Options), a novel hierarchical reinforcement learning framework designed to address the challenges of long-term sparse reward environments. MANGO decomposes complex tasks into multiple layers of abstraction, where each layer defines an abstract state space and employs options to modularize trajectories into macro-actions. These options are nested across layers, allowing for efficient reuse of learned movements and improved sample efficiency. The framework introduces intra-layer policies that guide the agent's transitions within the abstract state space, and task actions that integrate task-specific components such as reward functions. Experiments conducted in procedurally-generated grid environments demonstrate substantial improvements in both sample efficiency and generalization capabilities compared to standard RL methods. MANGO also enhances interpretability by making the agent's decision-making process transparent across layers, which is particularly valuable in safety-critical and industrial applications. Future work will explore automated discovery of abstractions and abstract actions, adaptation to continuous or fuzzy environments, and more robust multi-layer training strategies.

Matteo Cederle, Andrea Mazzucco, Andrea Demartini et al.

Electric vehicles (EV) charging stations are one of the critical infrastructures needed to support the transition to renewable-energy-based mobility, but ensuring their reliability and efficiency requires effective anomaly detection to identify irregularities in charging behavior. However, in such a productive scenario, it is also crucial to determine the underlying cause behind the detected anomalies. To achieve this goal, this study investigates unsupervised anomaly detection techniques for EV charging infrastructure, integrating eXplainable Artificial Intelligence techniques to enhance interpretability and uncover root causes of anomalies. Using real-world sensors and charging session data, this work applies Isolation Forest to detect anomalies and employs the Depth-based Isolation Forest Feature Importance (DIFFI) method to identify the most important features contributing to such anomalies. The efficacy of the proposed approach is evaluated in a real industrial case.

Elnur Isgandarov, Matteo Cederle, Federico Chiariotti et al.

Shared mobility systems, such as bike-sharing networks, play a crucial role in urban transportation. Identifying anomalies in these systems is essential for optimizing operations, improving service reliability, and enhancing user experience. This paper presents an interpretable anomaly detection framework that integrates multi-source data, including bike-sharing trip records, weather conditions, and public transit availability. The Isolation Forest algorithm is employed for unsupervised anomaly detection, along with the Depth-based Isolation Forest Feature Importance (DIFFI) algorithm providing interpretability. Results show that station-level analysis offers a robust understanding of anomalies, highlighting the influence of external factors such as adverse weather and limited transit availability. Our findings contribute to improving decision-making in shared mobility operations.

Manuel Barusco, Francesco Borsatti, Arianna Stropeni et al.

VAD is a critical field in machine learning focused on identifying deviations from normal patterns in images, often challenged by the scarcity of anomalous data and the need for unsupervised training. To accelerate research and deployment in this domain, we introduce MoViAD, a comprehensive and highly modular library designed to provide fast and easy access to state-of-the-art VAD models, trainers, datasets, and VAD utilities. MoViAD supports a wide array of scenarios, including continual, semi-supervised, few-shots, noisy, and many more. In addition, it addresses practical deployment challenges through dedicated Edge and IoT settings, offering optimized models and backbones, along with quantization and compression utilities for efficient on-device execution and distributed inference. MoViAD integrates a selection of backbones, robust evaluation VAD metrics (pixel-level and image-level) and useful profiling tools for efficiency analysis. The library is designed for fast, effortless deployment, enabling machine learning engineers to easily use it for their specific setup with custom models, datasets, and backbones. At the same time, it offers the flexibility and extensibility researchers need to develop and experiment with new methods.